# 특이값 분해

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## 노트

- a numeric or complex matrix whose SVD decomposition is to be computed.
^{[1]} - The singular value decomposition plays an important role in many statistical techniques.
^{[1]} - SVD can be used to find a generalized inverse matrix.
^{[2]} - Then, using SVD, we can essentially compress the image.
^{[2]} - PCA can be achieved using SVD.
^{[2]} - Multi-dimensional scaling can also be achieved using SVD.
^{[2]} - Calculating the SVD consists of finding the eigenvalues and eigenvectors of AAT and ATA.
^{[3]} - The final section works out a complete program that uses SVD in a machine-learning context.
^{[4]} - SVD is known under many different names.
^{[4]} - We have already seen in Equation (6) how an SVD with a reduced number of singular values can closely approximate a matrix.
^{[4]} - Because n is large, however, the algorithm takes too long or is unstable, so we want to reduce the number of variables using SVD.
^{[4]} - In this paper, we modify a classical downdating SVD algorithm and reduce its complexity significantly.
^{[5]} - Perhaps the most known and widely used matrix decomposition method is the Singular-Value Decomposition, or SVD.
^{[6]} - All matrices have an SVD, which makes it more stable than other methods, such as the eigendecomposition.
^{[6]} - The SVD is calculated via iterative numerical methods.
^{[6]} - The singular value decomposition (SVD) provides another way to factorize a matrix, into singular vectors and singular values.
^{[6]} - In this article, I will try to explain the mathematical intuition behind SVD and its geometrical meaning.
^{[7]} - To understand SVD we need to first understand the Eigenvalue Decomposition of a matrix.
^{[7]} - Before talking about SVD, we should find a way to calculate the stretching directions for a non-symmetric matrix.
^{[7]} - Now we can summarize an important result which forms the backbone of the SVD method.
^{[7]} - The SVD also captures indirect connections.
^{[8]} - The transaction item matrix is centered, scaled, and divided by nTran minus 1 before the singular value decomposition is carried out.
^{[8]} - The SVD implementation takes advantage of the sparsity of the transaction item matrix.
^{[8]} - Otherwise, it can be recast as an SVD by moving the phase of each σ i to either its corresponding V i or U i .
^{[9]} - The singular value decomposition can be used for computing the pseudoinverse of a matrix.
^{[9]} - The SVD can be thought of as decomposing a matrix into a weighted, ordered sum of separable matrices.
^{[9]} - The SVD can be used to find the decomposition of an image processing filter into separable horizontal and vertical filters.
^{[9]} - SVD allows us to extract and untangle information.
^{[10]} - In this article, we will detail SVD and PCA.
^{[10]} - SVD gives you the whole nine-yard of diagonalizing a matrix into special matrices that are easy to manipulate and to analyze.
^{[10]} - Let’s introduce some terms that frequently used in SVD.
^{[10]} - Here the SVD is used to perform a pseudoinverse of an otherwise ill-conditioned operator.
^{[11]} - For image processing and large scale inverse problems this requires the SVD of a large matrix.
^{[11]} - SVD is suited to regularisation because one has access to the singular values of the operator.
^{[11]} - Another feature of SVD is that it reveals the rank of the operator, useful in many imaging algorithms and signal processing applications.
^{[11]} - The most fundamental dimension reduction method is called the singular value decomposition or SVD.
^{[12]} - The SVD is a matrix decomposition, but it is not tied to any particular statistical method.
^{[12]} - SVD and Signal Processing II: Algorithms, Analysis and Applications, edited by R. Vaccaro, Elsevier Science Publishers, North Holland, 1991.
^{[13]} - x a numeric or complex matrix whose SVD decomposition is to be computed.
^{[14]} - There are a few caveats one should be aware of before computing the SVD of a set of data.
^{[15]} - The svd function computes the singular value decomposition of the SST dataset weighted over the cosine of the latitude.
^{[15]} - A weight term, however, is not necessary to complete the SVD analysis.
^{[15]} - This will remove the normalized eigenvector variable selection and return you to the SVD page.
^{[15]} - The SVD represents the essential geometry of a linear transformation.
^{[16]} - Recall that the diagonal elements of the Σ matrix (called the singular values) in the SVD are computed in decreasing order.
^{[16]} - In SAS, you can use the SVD subroutine in SAS/IML software to compute the singular value decomposition of any matrix.
^{[16]} - To save memory, SAS/IML computes a "thin SVD" (or "economical SVD"), which means that the U matrix is an n x p matrix.
^{[16]} - SVD produces two sets of orthonormal bases (U and V).
^{[17]} - The singular value decomposition (SVD) is a generalization of the algorithm we used in the motivational section.
^{[18]} - As in the example, the SVD provides a transformation of the original data.
^{[18]} - It is not immediately obvious how incredibly useful the SVD can be, so let’s consider some examples.
^{[18]} - Let’s compute the SVD on the gene expression table we have been working with.
^{[18]} - This chapter describes gene expression analysis by Singular Value Decomposition (SVD), emphasizing initial characterization of the data.
^{[19]} - Gene expression data are currently rather noisy, and SVD can detect and extract small signals from noisy data.
^{[19]} - SVD and PCA are common techniques for analysis of multivariate data, and gene expression data are well suited to analysis using SVD/PCA.
^{[19]} - In section 1, the SVD is defined, with associations to other methods described.
^{[19]}

### 소스

- ↑
^{1.0}^{1.1}R Documentation - ↑
^{2.0}^{2.1}^{2.2}^{2.3}Examples of Singular Value Decomposition | R Code Fragments - ↑ Singular Value Decomposition (SVD) tutorial
- ↑
^{4.0}^{4.1}^{4.2}^{4.3}Singular Value Decomposition (SVD) Tutorial: Applications, Examples, Exercises - ↑ A fast and stable algorithm for downdating the singular value decomposition
- ↑
^{6.0}^{6.1}^{6.2}^{6.3}How to Calculate the SVD from Scratch with Python - ↑
^{7.0}^{7.1}^{7.2}^{7.3}Understanding Singular Value Decomposition and its Application in Data Science - ↑
^{8.0}^{8.1}^{8.2}Singular Value Decomposition - ↑
^{9.0}^{9.1}^{9.2}^{9.3}Singular value decomposition - ↑
^{10.0}^{10.1}^{10.2}^{10.3}Machine Learning — Singular Value Decomposition (SVD) & Principal Component Analysis (PCA) - ↑
^{11.0}^{11.1}^{11.2}^{11.3}Singular Value Decomposition - an overview - ↑
^{12.0}^{12.1}16.1 - Singular Value Decomposition - ↑ Singular Value Decomposition
- ↑ R: Singular Value Decomposition of a Matrix
- ↑
^{15.0}^{15.1}^{15.2}^{15.3}Singular Value Decomposition - ↑
^{16.0}^{16.1}^{16.2}^{16.3}The singular value decomposition: A fundamental technique in multivariate data analysis - ↑ Singular Value Decomposition
- ↑
^{18.0}^{18.1}^{18.2}^{18.3}Singular Value Decomposition - ↑
^{19.0}^{19.1}^{19.2}^{19.3}Singular value decomposition and principal component analysis

## 메타데이터

### 위키데이터

- ID : Q420904

### Spacy 패턴 목록

- [{'LOWER': 'singular'}, {'LOWER': 'value'}, {'LEMMA': 'decomposition'}]
- [{'LEMMA': 'SVD'}]
- [{'LOWER': 'singular'}, {'LOWER': 'value'}, {'LOWER': 'decomposition'}, {'OP': '*'}, {'LEMMA': 'SVD'}]